A practical method for combining multivariate data in radio ...

2013 IEEE 24th International Symposium on Personal, Indoor and Mobile Radio Communications: Fundamentals and PHY Track

A practical method for combining multivariate data in radio environment mapping Jaakko Ojaniemi1 , Juha Kalliovaara2 , Jussi Poikonen1 , Risto Wichman1 1

Aalto University, School of Electrical Engineering, Finland 2 University of Turku, BID Technology, Finland

Abstract—In a cognitive radio system, awareness of the prevailing radio environment of the primary network, such as digital terrestrial television, is important since it governs the emission limits for the secondary system devices. Field strength estimates of the primary network are typically computed using terrain based radio propagation models, or by using univariate interpolation techniques to approximate the field strength from measurement samples. However, the limited geographical information or small numbers of measurement samples sets a restriction on the accuracy of the field strength estimates. In this paper, we propose a multivariate interpolation method for incorporating field measurements into radio propagation models. The proposed method shows considerable increase in estimation accuracy compared to previously presented methods. The model is verified using field measurement data from an operational digital terrestrial television network. Index Terms—radio environment map, cokriging, propagation model, field measurements

I. I NTRODUCTION In recent years the demand for wireless spectrum has been growing rapidly due to new commercial technologies and applications. To access more spectrum, cognitive radio (CR) techniques are able to take advantage of unutilized or underutilized spectrum, called white space (WS), within a primary network such as digital terrestrial television (DTT). Cognitive radio systems can allocate the unused spectrum, or alternatively cognitive radios can coexist on previously reserved frequency bands as secondary users. In a notion of radio environment mapping (REM) [2] a centralized database stores information about the state of the radio environment. The information can be of various types including, for example, locations of transmitters and receivers, field strength estimates for the operated network, results from field measurement campaigns, or measurement reports from static or mobile remote sensors such as white-space devices (WSDs). This information is combined and processed to give a realistic estimate of the prevailing radio environment. The accuracy of REM ensures the protection of the primary network operation; the field strength estimates of the primary network are used to calculate location specific maximum emission limits for WSDs, for example using the guidelines presented by the European Electronic Communications Committee (ECC) [1]. Therefore, realistic knowledge of the radio environment secures that the interference towards the primary network remains within acceptable limits while maximizing the throughput of the secondary system. Thus, efficient tech-

978-1-4577-1348-4/13/$31.00 ©2013 IEEE

729

niques for utilizing the information in a REM database need to be developed. Recently, geostatistical modeling in REM has been widely studied. In [3], a signal strength map was constructed by kriging interpolation using spatial dependency characteristics of field measurements. Reference [4] compared inverse distance weighted interpolation strategies for constructing a radio environment map from a limited number of measurement samples. The study in [5] described geostatistic technique to estimate the field strength and coverage of an operational WiMAX network using systematic sampling grid. In [6], deficiencies arising from using systematic sampling were overcome by designing a technique for finding a sampling pattern which minimizes the average interpolation error variance. The previous work on REM estimation has focused solely on univariate interpolation strategies to approximate the field strength in unmeasured locations. With these techniques the limited number of measurement samples restricts the accuracy of the field strength estimates. In this paper, we propose an efficient technique for improving the REM estimation in scenarios where relatively small numbers of measurement samples are available. The proposed multivariate kriging method utilizes correlated secondary information obtained from a terrain based propagation prediction model [7] to complement the measurement data. This paper shows that considerable improvement in prediction accuracy is achieved compared to univariate interpolation methods. The modeling procedure is verified with an extensive measurement campaign performed in an operational digital terrestrial television (DTT) test network. The rest of the paper is organized as follows: Section II presents the underlying geostatistical theory of the proposed modeling procedure. Section III describes a technique of applying the presented geostatistical methods for incorporating radio propagation model and field measurements. Section IV presents results and analysis, and conclusions are presented in Section V. II. G EOSTATISTICAL MODELING METHODS A. Variogram An experimental variogram describes the spatial autocorrelation structure of data, and it is used to represent the behaviour of a variable as a function of distance. The experimental

semivariogram is defined as [8]: n(h) 2 1  z(si ) − z(si + h) , γ(h) = 2n(h) i=1

The experimental cross-variogram function of the target and a single covariable is: (1)

where the lag distance h for irregularly spaced data is usually chosen as the average spacing between neighboring samples, z is the sampled value at the location si , and n(h) is the number of point pairs of observations separated by lag distance h. In this paper, for simplicity, we use the term variogram also for (1), although the variogram is commonly denoted as 2γ(h). The experimental variogram is fitted to a predefined variogram model, for example using the least squares method, to ensure that the estimation variance is positive and well-defined for all lag classes. There are several options for the variogram model, and the choice is typically made based on heuristics or on minimizing some error criterion. B. Ordinary kriging In ordinary kriging (OK) the predicted value is a weighted linear combination of the sample values, where the weights are found by minimizing the estimation variance. The OK estimator may be written as: zˆ(s0 ) =

N 

λi z(si ),

(2)

i=1

where N is the number of measurement samples contributing to  the estimate zˆ, and the weights λ are constrained so that i λi = 1. Minimizing the error variance results in the OK system: N 

λi γ(si , sj ) + φ = γ(sj , s0 ), j = 1, 2 . . . N

(3)

i=1

n(h)   1  z1 (si ) − z1 (si + h) z2 (si ) − z2 (si + h) . γ(h) = 2n(h) i=1 (4) The fitted cross-variogram model must satisfy the CauchySchwarz relation to ensure a positive estimation variance, i.e.:  ∀h > 0. |γ12 (h)| ≤ γ1 (h)γ2 (h),

The cokriging esimator is zˆ(s0 ) =

N1 

λm z1 (sm ) +

m=1

N2 

λn z2 (sn ),

(5)

n=1

where N1 and N2 are the number of samples, and λm , λn are the solved weights for the target and covariable. Minimization 2 [7, p.146] for two variables results of the error variance σE in the following set of linear equations: ⎧  N1  N2 ⎪ m=1 λm γ11 (sk , sm ) + n=1 λn γ12 (sk , sn ) + φ1 ⎪ ⎪ ⎪ = γ (s , s ), k = 1, 2 . . . N1 ⎪ 11 ⎪  N2 k 0 ⎨  N1 λ γ (s , s ) + λ γ (s , s m=1 m 21 l m n=1 n 22 l n ) + φ2 ⎪ = γ l = 1, 2 . . . N2 21 (sl , s0 ), ⎪  ⎪ ⎪ ⎪ λ = 1 ⎪ ⎩ m m = 0, n λn (6) where γuv represents the cross-variogram between target and covariable, φ1,2 are the Lagrange parameters, and the latter two equations ensure that the estimator is unbiased. As in OK, the weights are found by solving the kriging system with respect to λm,n . D. Spatial simulated annealing

where γ(si , sj ) is the value of the theoretical variogram fitted to (1) for a distance si −sj , and φ is the additional Lagrange parameter related to the constrain on the weights. Thus, to obtain the weights we need to solve (3) with respect to λ and take into account the constraint on the weights. C. Cokriging Multivariable kriging or cokriging (CK) is a method where a secondary variable (covariable) is used to predict the target variable in unsampled locations. To be successful, cokriging requires that the target and covariable(s) have an identifiable spatial structure (variogram or covariance) and spatially dependendent cross-correlation (cross-variogram or cross-covariance). The spatial structure and cross-correlation of a covariable are determined in a process called coregionalization, which must lead to a positive definite cokriging system [8]. Easiest way to ensure this is a linear model of coregionalization, where the direct and cross-variogram have the same shape and range, whereas can have different minimum and maximum values for the variogram function. The coregionalization and successive interpolation can be performed for an arbitrary number of variables. However, only a single covariable are considered in this paper.

730

Spatial simulated annealing (SSA) [9] is an iterative search algorithm for finding a global minimum for an objective function. In this paper, we apply the SSA algorithm to find locations for a given limited number of measurement points by minimizing the mean shortest distance between the sampling point and an arbitrary chosen location in the test area. This ensures a maximal coverage for interpolation. 1) Algorithm: Consider a combinatorial optimization problem where the objective function Φ has to be minimized. Starting with a random sampling scheme S0 , in which the sampling points are spread randomly within the search area, schemes Si and Si+1 with objective functions Φ(Si ) and Φ(Si+1 ), respectively, represent two outcomes of the optimization process. In simulated annealing the scheme Si+1 is derived by randomly perturbing one of the variables in Si , with probability P of accepting Si+1 given by  P(Si → Si+1 ) = 1,

Φ(Si+1 ) ≤ Φ(Si ) Φ(Si )−Φ(Si+1 ) P(Si → Si+1 ) = exp , Φ(Si+1 ) > Φ(Si ) T where T is a control parameter, in simulated annealing known as the system temperature, which is decreased as the optimization progresses. A new control parameter value is obtained

with T → αT where the constant α is smaller than, but close to, unity [9]. In addition, the number of total transitions or accepted transitions for a given value of T , and the stopping criterion of the process are specified explicitly. Accepting also sampling schemes which increase the objective function ensures that the process avoids being confined to a local minimum. 2) Objective function: In this study, we consider the minimization of the mean shortest distance (MMSD) as the objective funtion. In case of MMSD, the sampling points are spread regularly over the sampling array. Thus, the expectation of the distances between an arbitrary chosen pixel in the studied area and its nearest sampling point is minimized. The MMSD objective function is given by ΦMMSD (S) =

Ne 1  xi − sj  Ne i=1

(7)

where Ne is the number of possible evaluation points, and the Euclidean distances are calculated between the pixel xi and its nearest sampling point sj ∈ S. Depending on the value of the objective function in sampling scheme S the SSA algorithm moves one observation point s ∈ S to a new location, restricted by the street network, and proceeds the optimization process. III. S IMULATION AND MEASUREMENTS

Transmission parameters ERP Antenna height (ground/sea) Location Polarization Frequency ITU-R P.1812 parameters Time percentage Location probability

Value 200 W 40 m / 54 m 22E1533 / 60N2702 Horizontal 610 MHz 1% 60 %

TABLE I T EST TRANSMISSION CONFIGURATION

measurements can be performed in a relatively small area; the number of measurement locations are limited to 5, and the study area to a 2 km × 2 km square region. Thus, we show an example of a situation where the resources for sampling the target variable are strongly constrained. The northwest corner of the study region corresponds to the location of the DTT transmitter. To find the sample pattern by MMSD criterion, the SSA algorithm is used to minimize the mean shortest distance between the sampling point sj and the possible evaluation point xi , while the evaluation locations are drawn from an extensive set of previously measured locations described in III-B. Possible sampling locations are limited to the street network shown in Fig. 1. The figure also shows the sampling locations chosen by the SSA algorithm.

A. Radio propagation model as a covariable

731

Street network Measurement point

60.4497 60.4477 60.4457 60.4437 Latitude

Cokriging requires information of the covariable either sampled on the same or (partially) different locations. In this study, field strength measurements are considered as the target variable to be estimated, and the covariable is provided by a propagation prediction model of the measured network. The propagation prediction is implemented according to the guidelines presented in [7]. In addition to basic freespace propagation loss including short-term effects, the implemented model considers corrections due to different kinds of radio propagation phenomena. These include diffraction, tropospheric scatter, ducting and layer reflection/refrection, local clutter height, location variability, and building entry loss. Calculating the additional corrections to the basic propagation loss are performed by using information from a digital elevation model (DEM) and clutter height (building data with 4 height classes), both with a spatial resolution of 5 m × 5 m. Using detailed geographical information and accurate propagation modeling allows the prediction to be performed in a precision needed for cokriging; according to [10] the correlation coefficient between the target and the covariable must lie well above 0.6 for succesfully utilizing the provided coinformation. In our study, a correlation ρ = 0.75 between the propagation model and field measurements was observed. The SSA algorithm is used to find such locations for field measurements that maximize the coverage while the possible sampling locations are restricted to the street network. In particular, we consider a case where a limited number of

60.4417 60.4397 60.4377 60.4357 60.4337

22.2534

22.2573

22.2612

22.2651 Longitude

22.269

22.2729

22.2769

Fig. 1. Measurement points for target variable determined by using the SSA algorithm for spreading the points regularly over the sampling array.

B. Field measurements and test network In this study, we use the measurements from an operational DTT test network [6]. In short, the test network in Turku, Finland, operates on channel 38 (610 MHz) and covers a relatively large geographical area and diverse environments including urban, suburban and rural locations. In the measurement campaign, approximately 6500 geolocation pixels of size 5 m × 5 m were measured, each including 200-1200 samples, and the median sample value for each geolocation was chosen

a) ITU−R P.1812

b) MMSD, OK 140 130

50

75

50

120 100

100 110

200

90

250

80

150 200

65

dB(μV/m)

100

70 dB(μV/m)

150

250

70 300

60

300 60

350

MAE: 5.0268 MSE: 36.5322

400 100

200

300

350

50 40

MAE: 4.2674 MSE: 28.1493

400

400

100

c) MMSD, CK (10 secondary samples)

200

300

55

400

d) MMSD, CK (50 secondary samples) 75

50

50

100

75

100

70

250

150 65

200

dB(μV/m)

65

200

dB(μV/m)

70 150

250 60

60 300

300

350

MAE: 4.2406 MSE: 27.4179

400 100

200

300

55

350

55

MAE: 4.1672 MSE: 26.4821

400

400

50 100

200

300

400

Fig. 2. Estimated field strength values for the test area. In a) the estimation is based on the propagation prediction model. In b) the estimation is performed by interpolating the MMSD optimized sampling scheme using the OK method. In c) and d) the sampling locations are found by MMSD, and the field strength estimates for unsampled locations are determined by CK, with covariate information drawn from a radio propagation model represented by a), using 10, c), and 50, d), nearest covariate samples for each evaluation point.

to be used in the subsequent interpolation. The measured received signal strength indication (RSSI) values, expressed in dBmW, were converted to the corresponding electric field strength values by taking into account the additional receiver gains and losses. This allows a consistent comparison between the used radio propagation model and the measurement data. The transmission parameters are summarized in Table I. IV. R ESULTS The locations for the target variable were found by SSA algorithm and the corresponding samples were chosen from the measurement set, as described in III-A. The sampling array was then used in OK and CK interpolation. In OK, all 5 target values were used for each estimation point. In CK, additional 10 or 50 nearest covariable values were sampled from the radio prediction model. Figure 2 shows the estimated field strength for the test area using different modeling techniques.

732

The verification is performed by comparing the estimated field strengths to the entire set of field measurement results, which comprises of approximately 6800 geolocation pixels. However, to distinguish the performance of the CK in areas where the target variable is undersampled, we show the comparison results for the southeast quarter of the estimation surface which contains approximately 1800 sampled geolocation pixels. This quarter is furthest away from the measurement locations used in the interpolation, as seen from Fig. 1. Although the radio propagation model was configured according to the measurement data to give zero mean error over the whole sample set, the error is still relatively large in the quarter furthest away from the transmitter. This is due to inaccuracies in the geographical data, whose effects accumulate along with the increasing propagation path length. On the other hand, also the OK suffers from an inaccuracy;

after a distance greater than the range of the variogram function the weights for the sample points are fixed, and do not provide additional information for the prediction value. Cokriging estimator is a linear combination of the two, and thus provides a sufficient compromise in areas where the primary variable is undersampled. The performance of the modeling techniques is measured in terms of mean absolute error (MAE) and variance of the error, described by the mean squared error (MSE), between predicted and measured values. The proposed method (Fig. 2–c,d) shows approximately 2.6% - 6% decrease in MSE compared to univariate kriging (Fig. 2–b), and a considerable decrease in MSE, 28%, compared to a radio propagation model (Fig. 2–a). Similar results are observed also for other quarter parts in the area boundary. However, the achieved correlation, ρ = 0.75, between the radio propagation model and field measurements is evidently insufficient; by performing the verification over the whole sample set in the map area (6800 measured geolocation pixels) the CK method did not provide further improvements compared to OK, that is, the error statistics are equivalent. The efficiency of the CK method can be further increased by using more accurate propagation modeling to increase the correlation, however, it requires the use of high-resolution geographical information which may not be available. Therefore, the CK method is especially practical for estimating the field strength in boundary parts of the prediction surface where measurement locations are distant or unavailable, and additional accuracy of signal strength estimation is needed. For example, in CR systems such conditions may exist near coverage borders which are critical to avoid co-channel interference and to determine the adjacency of a particular communications channel. V. C ONCLUSION This paper described a practical multivariate interpolation method for combining radio propagation models and field measurement data. Considerable improvement in the accuracy of the signal strength predictions was obtained compared to either propagation prediction or univariate interpolation. Results from an extensive measurement campaign were used in the verification. The proposed method is especially practical in scenarios where relatively small numbers of measurement samples are available or the sampling locations are distant, and additional accuracy in the boundaries of the prediction surface is needed. ACKNOWLEDGEMENTS This work was funded by Tekes, the Finnish Funding Agency for Technology and Innovation, in the WISE project [11] as the part of Trial technology program, and by the Academy of Finland (133888). R EFERENCES [1] “Technical and operational requirements for the possible operation of cognitive radio systems in the white spaces of the frequency band 470790 MHz,” ECC Report 159, January 2011. Available online through http://www.erodocdb.dk

733

[2] Zhao, Y., Morales, L., Gaeddert, J., Bae, K.K., Jung-Sun Um, Reed, J.H., “Applying Radio Environment Maps to Cognitive Wireless Regional Area Networks,” Proc. IEEE Symposium on New Frontiers in Dynamic Spectrum Access Networks, DySPAN 2007, Dublin, Ireland, April 2007. [3] Riihijarvi, J., Mahonen, P.,Wellens, M., Gordziel, M. “Characterization and modelling of spectrum for dynamic spectrum access with spatial statistics and random fields,” Proc. IEEE 19th International Symposium on Personal, Indoor and Mobile Radio Communications, Cannes, France, Sept. 2008 [4] Denkovski, D., Atanasovski, V., Gavrilovska, L., Riihijarvi, J., Mahonen, P. , ”Reliability of a radio environment Map: Case of spatial interpolation techniques,” Proc. 7th International ICST Conference on Cognitive Radio Oriented Wireless Networks and Communications (CROWNCOM) 2012, Stockholm, Sweden, June 2012. [5] Phillips, C., Ton M., Sicker, D., Grunwald, D., ”Practical Radio Environment Mapping with Geostatistics,”’ Proc. IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks, DySPAN 2012, Bellevue, Washington, USA, October 2012. [6] Ojaniemi, J., Kalliovaara, J., Alam, A., Poikonen, J., Wichman, R., ”Optimal field measurement design for radio environment mapping,” Proc. 47th Annual Conference on Information Sciences and Systems, CISS 2013, Baltimore, USA, March 2013. [7] “A path-specific propagation prediction method for point-to-area terrestrial services in the VHF and UHF bands,” ITU-R Recommendation P.1812-2, June 2012. Available online through http://www.itu.int/rec/RREC-P.1812-2-201202-I/en [8] Wackernagel, H., Multivariate Geostatistics, Springer, Berlin, 1995. [9] Van Groenigen, J.W., Stein, A., ”Constrained Optimization of Spatial Sampling using Continuous Simulated Annealing,” Journal of Environmental Quality, Vol. 27, Issue 5, September 1998. [10] Rossiter, D.G., ”Technical Note: Co-kriging with the Gstat package of the R environment for statistical computing”, University of Twente, Faculty of Geo-Information Science & Earth Observation (ITC), Enschede, NL [11] WISE project, http://wise.turkuamk.fi